It is well known that many primary students have difficulty in learning mathematics in our base ten system. Students also now need to become familiar with and learn to use a base two system but this is normally reserved for higher grades. The current invention provides a math manipulative system for teachers and students.
With this manipulative device, a child can both DO and SEE simple mathematical calculations.
The kit may be summarized as including a vertical cube stack with different sized angled sticks to allow a teacher to move cubes to indicate simple mathematical functions and their interrelations with the cubes allowing a student to actually visualize each operation. There is also available a Child training unit that allows the child to both do and see simple operations.
The current invention is comprised of a Cube Calculator(trademark) mathematics manipulative device, its accessories, and related methods.
The Cube Calculator is a manipulative tool which has a plurality of slots, where each slot holds an object such as a colored cube. The slots are typically arranged in a stacked fashion so that each slot is presented from right to left relative to the student. By moving the object from a rest position, typically on the student""s left, to an active position, typically on the student""s right, the object represents a value associated with the slot. The value is typically assigned by a corresponding number line or numbered bar which has a plurality of indicia presented in proximity to the slots. For instance, the Cube Calculator may have 25 slots, and a numbered bar with the numerals 1 through 25 presented on the stick.
The Cube Calculator is arranged so that the items in the calculator are arranged in easily discernable groups of five. Typically, the grouping is by color, and alternately the distinctions between the groups of five may be made by texture, shape, or pattern. This grouping by fives creates a natural break for the human eye, and the human mind, which is complimentary to the base ten counting system of mathematics. The groupings may be rapidly examined. This grouping by five has many analogies including tally marks, Roman numerals, the five digits on a human hand, and the minute markings on the face of a clock.
For example, if you ask a small child to show you xe2x80x9csevenxe2x80x9d, the child is likely to hold up five fingers on one hand and two fingers on another hand. It would be very unusual for the child to show three fingers and four fingers on another hand. This is the concept of xe2x80x9cbreakingxe2x80x9d a number over multiples of five or ten. This breaking is useful in basic arithmetic operations and is closely related to the concepts of xe2x80x9cborrowingxe2x80x9d and xe2x80x9cregroupingxe2x80x9d in addition and subtraction problems.
When students manipulate the cubes, or other objects, in sets of five, the device reveals to them the efficient ways to break basic numerals around familiar multiples of five or ten. Technically this is called xe2x80x9cmakingxe2x80x9d and xe2x80x9cbreakingxe2x80x9d the numerals into two xe2x80x9caddendsxe2x80x9d. For example if we were adding the number eight (8) to something there are several ways that we could break the particular eight that is being added- such as 7+1, 6+2, 5+3, 4+4, etc. If students are adding the number eight (8) to another number the most useful particular set of addends may change. For example when adding eight to sixteen, it is most convenient to first add four to get to the number twenty which is a multiple of ten and then to add the other four to get the answer twenty-four:
16+8=
16+(4+4)=
(16+4)+4=
20+4=24
On the other hand, if the number eight was added to the number twenty-four, then it is convenient to think of this eight as being first in a group of six and then an additional two. The first six getting to the number thirty which is a multiple of ten and the remaining two getting to the answer thirty-two:
24+8=
24+(6+2)=
xe2x80x83(24+6)+2=
30+2=32 